The City School. PECHS Boys Campus. Summer Pack 2018 for Class 8. Area and Perimeter. Area of rectangle = length breadth

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1 The City School PECHS Boys Campus Area and Perimeter Summer Pack 2018 for Class 8 Area of rectangle = length breadth Area of square = length length Area of triangle = 1/2 base height Q1 Find the area and perimeter of shaded region. Q2 Calculate the shaded area (a) (b)

2 Q3 Calculate area and Perimeter for each polygon. Watch this video for understanding the basic skills to find area and perimeter

3 Misconception: You must add the boundry for the perimeter. Not the inner lines Game for Area and Perimeter

4 Shapes and Polygons Q1 The following formulae for regular polygons should be known: Exterior angle = 360º no. of sides Interior angle = 180º - exterior angle Sum of interior angles = 180 x (no. of sides - 2) Example A regular polygon has an interior angle of 165.6º. How many sides does it have? Answer Exterior angle = interior angle = = 14.4º No. of sides = 360 exterior angle = = 25 The following link will help you to find angle in a polygon. Video from Khan academy Q2 Find the number of sides of a regular polygon with an exterior angle of 45 o. Q3 Calculate the value of x for the following figures.

5 Q4 Find the unknown angle for each of the following figure. Q5 Q6 Find the size of each interior angle in the above pentagon. Three identical regular pentagon are joined together in the above diagram. Work out for y.

6 Q7 Shown below is a regular hexagon ABCDEF. Calculate angle x. Q8 Shown below is a regular pentagon ABCDE. Find x and y. Q9 Show is a regular Hexagon and regular Octagon. Calculate the size of angle y.

7 Q10 Shown below is a regular hexagon, with an exterior angle labeled y. Find y. Q11 ABCDEFGH is a regular octagon. Calculate the size of angle AOB and ABC. Q12 Show below is an interior angle from a regular polygon. Calculate the number of side of the polygon has.

8 Angles Watch this videos from khan academy Q1 Calculate the value of x in the following figures This video from khan academy will help to find unknown angles in the triangles.

9 Q2 Calculate the value of x in the following figures. Q3 Show that whether the following figure is congruent or NOT. Q4 Triangle ABC is similar to JKL. Find the value of q.

10 Arithmetic Q1 Example: Two numbers are in the ratio 3 : 4. If the sum of numbers is 63, find the numbers. Solution: Sum of the terms of the ratio = = 7 Sum of numbers = 63 Therefore, first number = 3/7 63 = 27 Second number = 4/7 63 = 36 Therefore, the two numbers are 27 and 36. This video from khan academy helps you to develop basic skills of ratio and proportion. Q2 Q3 Q4 The ratio of monthly income to the savings in a family is 5 : 4 If the savings be $9000, find the income and the expenses. Two numbers are in the ratio 3 : 7. If their sum is 710, find the numbers. A sum of money is divided among Ron and Andy in the ratio 4 : 7. If Andy s share is $616, find the total money. Q5 Example A number is reduced by 100 %. Its present value is 270. What was its original value? Solution: Original value is percentage = 100 %. Reduce amount in percentage = 10 % Therefore, Percent value in percentage = 100 % - 10 % = 90 %. According to the problem, 90 % of original value = 270. Therefore, 100 % of original value = 270/ = 300. Thus, the original value was 300.

11 Q6 Q7 Q8 Q9 Q10 The price of rice is increased from $10 to $12.50 per kg. Find the percentage increase in price. The population in a small town increases from to in one year. Find the percentage increase in population. The cost of an article is decreased by 15%. If the original cost is $80, find the decrease cost. A television manufacturing company declares that a television is now available for $5600 as against $8400 one year before. Find the percentage reduction in the price of television offered by the company. A tank has 82 3 / 4 litres of water / 5 litres were used and the tank was filled with another 18 3 / 4 litres. What is the final volume of water in the tank? RATIOS AND PROPORTIONS INSTRUCTION SHEET Ratios A ratio is a comparison of two quantities that have the same units. You can express a ratio in any one of the following ways: 18:5 18 to 5 Example #1: If one store has 360 items and another store has 100 of the same items, express the ratio of the items. 360:100 or 360 to 100 Example #2: John earns $350 a week. His take-home pay, however, is $295. What is the ratio of his gross pay to his take-home pay. 350 = Rates A rate is a comparison of two quantities that have different units. Rates are usually expressed in the fractional form. Example: Francine paid $16 for her 12-month subscription to Better Homes and $16.00 = $4.00 Gardens magazine. Express as a rate.

12 12 magazines 3 magazines If Francine wants to know how much she pays for each (1) magazine, she can divide $4 by 3 magazines. This will give her the price per magazine (also called the unit rate). $4.00 = $1.33/magazine 3 Applied Proportion Problems Many problems can be solved by setting up a direct proportion (an increase in one quantity leads to a proportional increase in the other quantity) or by setting up equivalent rates. Example: In one day you earn $75 for 8 hours of work. If you work 37.5 hours for the week, what will your weekly pay be? 8 hours = $75 8 hours = 37.5 hours 37.5 hours x $75 x 8x = x = x = x = or x = x = x = $ x = $ RATIOS AND PROPORTIONS PRACTICE SHEET This video from khan academy will help you to solve ratio problems.

13 A. Write each ratio as a fraction in lowest terms to to : : : to : : : to B. Solve each proportion and give the answer in simplest form : 8 = n : = 8 7 n 3. n = : n = 6 : = = 12 n n 7. 2 ½ : 3 ½ = n : : 2 = n : to 8 = 15 to n : n = 3 : = n = n :19 = 14:n = 2 n : ¼ = n : ⅓ to 121 = n to 11 C. Solve by using a proportion. Round answers to the nearest hundredth if necessary. 1. You jog 3.6 miles in 30 minutes. At that rate, how long will it take you to jog 4.8 miles?

14 2. You earn $33 in 8 hours. At that rate, how much would you earn in 5 hours? 3. An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed? 4. What is the cost of six filters if eight filters cost $39.92? 5. If one gallon of paint covers 825 sq. ft., how much paint is needed to cover 2640 sq. ft.? 6. A map scale designates 1 = 50 miles. If the distance between two towns on the map is 2.75 inches, how many miles must you drive to go from the first town to the second? 7. Bob is taking his son to look at colleges. The first college they plan to visit is 150 miles from their home. In the first hour they drive at a rate of 60 mph. If they want to reach their destination in 2 ½ hours, what speed must they average for the remainder of their trip? 8. Four employees can wash 20 service vehicles in 5 hours. How long would it take 5 employees to wash the same number of vehicles?